Viking Results, 2021-05

# Check requisite packages are installed.
packages <- c(
  "plotly", 
  "dplyr"
)
for (pkg in packages) {
  library(pkg, character.only = TRUE)
}

package 㤼㸱plotly㤼㸲 was built under R version 4.0.5Loading required package: ggplot2
package 㤼㸱ggplot2㤼㸲 was built under R version 4.0.3Registered S3 method overwritten by 'data.table':
  method           from
  print.data.table     
Registered S3 methods overwritten by 'htmltools':
  method               from         
  print.html           tools:rstudio
  print.shiny.tag      tools:rstudio
  print.shiny.tag.list tools:rstudio
Registered S3 method overwritten by 'htmlwidgets':
  method           from         
  print.htmlwidget tools:rstudio

Attaching package: 㤼㸱plotly㤼㸲

The following object is masked from 㤼㸱package:ggplot2㤼㸲:

    last_plot

The following object is masked from 㤼㸱package:stats㤼㸲:

    filter

The following object is masked from 㤼㸱package:graphics㤼㸲:

    layout

package 㤼㸱dplyr㤼㸲 was built under R version 4.0.4
Attaching package: 㤼㸱dplyr㤼㸲

The following objects are masked from 㤼㸱package:stats㤼㸲:

    filter, lag

The following objects are masked from 㤼㸱package:base㤼㸲:

    intersect, setdiff, setequal, union

What do the results look like?

dirViking <- c(
  file.path(
    getwd(), "LCAB_LawMorton1996-NumericalPoolCommunityScaling"
  ),
  file.path(
    getwd(), "LCAB_LawMorton1996-NumericalPoolCommunityScaling2"
  )
)
dirVikingResults <- file.path(
  dirViking, c("results-2021-04", "save-2021-05-10") # Latter not 100% yet.
)
resultFormat <- paste0(
  "run-", 
  "%d", # Combination Number, or CombnNum.
  "-", 
  "%s", # Run Seed.
  ".RDS"
)

2021-04 Data

# Copied from LawMorton1996-NumericalPoolCommunityScaling-Calculation.R
# TODO: In the future, make this a separate file that everyone can call...
set.seed(38427042)

basal <- c(3, 10, 30, 100, 300, 1000)
consumer <- c(3, 10, 30, 100, 300, 1000) * 2
events <- (max(basal) + max(consumer)) * 2
runs <- 100

logBodySize <- c(-2, -1, -1, 1) # Morton and Law 1997 version.
parameters <- c(0.01, 10, 0.5, 0.2, 100, 0.1)

# Need to rerun seedsPrep to get the random number generation right for seedsRun
seedsPrep <- runif(2 * length(basal) * length(consumer)) * 1E8
seedsRun <- runif(runs * length(basal) * length(consumer)) * 1E8

paramFrame <- with(list(
  b = rep(basal, times = length(consumer)),
  c = rep(consumer, each = length(basal)),
  s1 = seedsPrep[1:(length(basal) * length(consumer))],
  s2 = seedsPrep[
    (length(basal) * length(consumer) + 1):(
      2 * length(basal) * length(consumer))
  ],
  sR = seedsRun
), {
  temp <- data.frame(
    CombnNum = 0,
    Basals = b,
    Consumers = c,
    SeedPool = s1,
    SeedMat = s2,
    SeedRuns = "",
    SeedRunsNum = 0,
    EndStates = I(rep(list(""), length(b))),
    EndStatesNum = 0,
    EndStateSizes = I(rep(list(""), length(b))),
    EndStateSizesNum = NA,
    EndStateAssembly = I(rep(list(""), length(b))),
    EndStateAbundance = I(rep(list(""), length(b))),
    Dataset = "2021-04",
    DatasetID = 1,
    stringsAsFactors = FALSE
  )
  for (i in 1:nrow(temp)) {
    seeds <- sR[((i - 1) * runs + 1) : (i * runs)]
    temp$SeedRuns[i] <- toString(seeds) # CSV
    temp$SeedRunsNum[i] <- length(seeds)
  }
  temp$CombnNum <- 1:nrow(temp)
  temp
})

# Note: n + 2 end states. Failure to finish, failure to obtain state, and state.
for (i in 1:nrow(paramFrame)) {
  resultsList <- list(
    "No Run" = 0,
    "No State" = 0
  )
  resultsSize <- list(
    "0" = 0
  )
  resultsAssembly <- list(
    "No Run" = data.frame(),
    "No State" = data.frame()
  )
  seeds <- unlist(strsplit(paramFrame$SeedRuns[i], ', '))
  for (seed in seeds) {
    fileName <- file.path(
      dirVikingResults[paramFrame$DatasetID[i]],
      sprintf(resultFormat, paramFrame$CombnNum[i], seed)
    )
    
    if (file.exists(fileName)) {
      temp <- load(fileName)
      temp <- eval(parse(text = temp)) # Get objects.
      
      if (is.data.frame(temp)) {
        community <- toString(
          temp[[ncol(temp)]][[nrow(temp)]]
        )
        size <- toString(length(temp[[ncol(temp)]][[nrow(temp)]]))
        
        if (community == "") {
          resultsList$`No State` <- resultsList$`No State` + 1
          resultsSize$`0` <- resultsSize$`0` + 1
          
        } else if (community %in% names(resultsList)) {
          resultsList[[community]] <- resultsList[[community]] + 1
          resultsSize[[size]] <- resultsSize[[size]] + 1
          
        } else {
          resultsList[[community]] <- 1
          resultsAssembly[[community]] <- temp
          
          if (size %in% resultsSize) {
            resultsSize[[size]] <- resultsSize[[size]] + 1
          } else {
            resultsSize[[size]] <- 1
          }
        }
      } else {
        resultsList$`No State` <- resultsList$`No State` + 1
        resultsSize$`0` <- resultsSize$`0` + 1
      }
    } else {
      resultsList$`No Run` <- resultsList$`No Run` + 1
      resultsSize$`0` <- resultsSize$`0` + 1
    }
  }
  
  paramFrame$EndStates[[i]] <- resultsList
  paramFrame$EndStatesNum[i] <- length(resultsList) - 2 # ! No State, No Run
  paramFrame$EndStateSizes[[i]] <- resultsSize
  paramFrame$EndStateSizesNum[i] <- length(resultsSize) - 1 # ! 0
  paramFrame$EndStateAssembly[[i]] <- resultsAssembly
}

2021-05 Data

source(
  file.path(getwd(), 
            "LawMorton1996-NumericalPoolCommunityScaling-Settings2.R")
)

oldNrow <- nrow(paramFrame)

paramFrame <- rbind(paramFrame, with(list(
  b = rep(basal, times = length(consumer)),
  c = rep(consumer, each = length(basal)),
  s1 = seedsPrep[1:(length(basal) * length(consumer))],
  s2 = seedsPrep[
    (length(basal) * length(consumer) + 1):(
      2 * length(basal) * length(consumer))
  ],
  sR = seedsRun
), {
  temp <- data.frame(
    CombnNum = 0,
    Basals = b,
    Consumers = c,
    SeedPool = s1,
    SeedMat = s2,
    SeedRuns = "",
    SeedRunsNum = 0,
    EndStates = I(rep(list(""), length(b))),
    EndStatesNum = 0,
    EndStateSizes = I(rep(list(""), length(b))),
    EndStateSizesNum = NA,
    EndStateAssembly = I(rep(list(""), length(b))),
    EndStateAbundance = I(rep(list(""), length(b))),
    Dataset = "2021-05",
    DatasetID = 2,
    stringsAsFactors = FALSE
  )
  for (i in 1:nrow(temp)) {
    seeds <- sR[((i - 1) * runs + 1) : (i * runs)]
    temp$SeedRuns[i] <- toString(seeds) # CSV
    temp$SeedRunsNum[i] <- length(seeds)
  }
  temp$CombnNum <- 1:nrow(temp)
  temp
})
)

# Note: n + 2 end states. Failure to finish, failure to obtain state, and state.
# Modified from above, but with the abundance recorded.
for (i in (oldNrow + 1):nrow(paramFrame)) {
  resultsList <- list(
    "No Run" = 0,
    "No State" = 0
  )
  resultsSize <- list(
    "0" = 0
  )
  resultsAssembly <- list(
    "No Run" = data.frame(),
    "No State" = data.frame()
  )
  resultsAbund <- list(
    "No Run" = "",
    "No State" = ""
  )
  seeds <- unlist(strsplit(paramFrame$SeedRuns[i], ', '))
  for (seed in seeds) {
    fileName <- file.path(
      dirVikingResults[paramFrame$DatasetID[i]],
      sprintf(resultFormat, paramFrame$CombnNum[i], seed)
    )
    
    if (file.exists(fileName)) {
      temp <- load(fileName)
      temp <- eval(parse(text = temp)) # Get objects.
      
      if (is.list(temp) && "Result" %in% names(temp)) {
        
        if (is.data.frame(temp$Result))
          community <- temp$Result$Community[[nrow(temp$Result)]]
        else 
          community <- temp$Result
        
        size <- toString(length(community))
        
        if (community[1] != "") 
          abund <- toString(temp$Abund[community + 1])
        else 
          abund <- ""
        
        community <- toString(community)
        
        if (community == "") {
          resultsList$`No State` <- resultsList$`No State` + 1
          resultsSize$`0` <- resultsSize$`0` + 1
          
        } else if (community %in% names(resultsList)) {
          resultsList[[community]] <- resultsList[[community]] + 1
          resultsSize[[size]] <- resultsSize[[size]] + 1
          
        } else {
          resultsList[[community]] <- 1
          resultsAssembly[[community]] <- temp
          resultsAbund[[community]] <- abund
          
          if (size %in% resultsSize) {
            resultsSize[[size]] <- resultsSize[[size]] + 1
          } else {
            resultsSize[[size]] <- 1
          }
        }
      } else {
        resultsList$`No State` <- resultsList$`No State` + 1
        resultsSize$`0` <- resultsSize$`0` + 1
      }
    } else {
      resultsList$`No Run` <- resultsList$`No Run` + 1
      resultsSize$`0` <- resultsSize$`0` + 1
    }
  }
  
  paramFrame$EndStates[[i]] <- resultsList
  paramFrame$EndStatesNum[i] <- length(resultsList) - 2 # ! No State, No Run
  paramFrame$EndStateSizes[[i]] <- resultsSize
  paramFrame$EndStateSizesNum[i] <- length(resultsSize) - 1 # ! 0
  paramFrame$EndStateAssembly[[i]] <- resultsAssembly
  paramFrame$EndStateAbundance[[i]] <- resultsAbund
}

Plot

# X, Y, Basal and Consumer.
# Z = Sizes of the Endstates.

plotScalingData <- data.frame(
  CombnNum = rep(paramFrame$CombnNum, paramFrame$EndStatesNum),
  Basals = rep(paramFrame$Basals, paramFrame$EndStatesNum),
  Consumers = rep(paramFrame$Consumers, paramFrame$EndStatesNum),
  Dataset = rep(paramFrame$Dataset, paramFrame$EndStatesNum),
  DatasetID = rep(paramFrame$DatasetID, paramFrame$EndStatesNum)
)

# Communities
comms <- unlist(lapply(paramFrame$EndStates, names))
freqs <- unlist(paramFrame$EndStates)
asmbl <- unlist(paramFrame$EndStateAssembly, recursive = FALSE)
asmbl <- asmbl[comms != "No Run" & comms != "No State"]
freqs <- freqs[comms != "No Run" & comms != "No State"]
comms <- comms[comms != "No Run" & comms != "No State"]

asmbl <- lapply(asmbl, function(d) {
  if ("Result.Outcome" %in% names(d))
    d %>% dplyr::filter(Result.Outcome != "Type 1 (Failure)" & 
                          Result.Outcome != "Present")
  else
    d$Result %>% dplyr::filter(Outcome != "Type 1 (Failure)" & 
                                 Outcome != "Present")
})

plotScalingData$Communities <- comms
plotScalingData$CommunityFreq <- freqs
plotScalingData$CommunitySeq <- asmbl

# Community Size
temp <- unlist(lapply(strsplit(plotScalingData$Communities, ','), length))
plotScalingData$CommunitySize <- temp

# For usage by the reader.

plotScaling <- plotly::plot_ly(
  plotScalingData,
  x = ~Basals,
  y = ~Consumers,
  z = ~CommunitySize,
  color = ~Dataset
)

plotScaling <- plotly::add_markers(plotScaling)

plotScaling <- plotly::layout(
  plotScaling,
  scene = list(
    xaxis = list(type = "log"),
    yaxis = list(type = "log")
  )
)

plotScaling

minimal value for n is 3, returning requested palette with 3 different levels
minimal value for n is 3, returning requested palette with 3 different levels
minimal value for n is 3, returning requested palette with 3 different levels
minimal value for n is 3, returning requested palette with 3 different levels

plotScalingData %>% dplyr::select(-CommunitySeq)

What happens if we try to plot a plane?

Check with dataset as a part of the model. (They should not be, as they are generated by the same code, but different seeds.)

plotSamplingDataLM1 <- lm(
  log(CommunitySize) ~ log(Basals) + log(Consumers) + Dataset, 
  data = plotScalingData
)
summary(plotSamplingDataLM1)

Call:
lm(formula = log(CommunitySize) ~ log(Basals) + log(Consumers) + 
    Dataset, data = plotScalingData)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.83712 -0.17860  0.01358  0.20886  0.78899 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)     0.91641    0.11947   7.670 5.05e-11 ***
log(Basals)     0.23818    0.02014  11.825  < 2e-16 ***
log(Consumers)  0.03652    0.01856   1.968   0.0528 .  
Dataset2021-05  0.07433    0.07197   1.033   0.3050    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.3089 on 75 degrees of freedom
Multiple R-squared:  0.677, Adjusted R-squared:  0.664 
F-statistic: 52.39 on 3 and 75 DF,  p-value: < 2.2e-16

Datasets do not look to have a statistically significant effect. Without comparing the models (would need to do in any publication), the model without the dataset effect is:

plotSamplingDataLM2 <- lm(
  log(CommunitySize) ~ log(Basals) + log(Consumers), 
  data = plotScalingData
)
summary(plotSamplingDataLM2)

Call:
lm(formula = log(CommunitySize) ~ log(Basals) + log(Consumers), 
    data = plotScalingData)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.86732 -0.17301 -0.02186  0.20156  0.74221 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)     0.93258    0.11850   7.870 1.95e-11 ***
log(Basals)     0.24312    0.01957  12.421  < 2e-16 ***
log(Consumers)  0.03800    0.01851   2.053   0.0435 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.309 on 76 degrees of freedom
Multiple R-squared:  0.6724,    Adjusted R-squared:  0.6638 
F-statistic: 77.99 on 2 and 76 DF,  p-value: < 2.2e-16

Adding this to the plot:

# E.g. https://stackoverflow.com/a/38533046
plotSamplingDataLM2Res <- 3
plotSamplingDataLM2AxisX <- sort(unique(plotScalingData$Basals))
  # seq(min(plotScalingData$Basals), 
  #                               max(plotScalingData$Basals),
  #                               by = plotSamplingDataLM2Res) 
plotSamplingDataLM2AxisY <- sort(unique(plotScalingData$Consumers))
# seq(min(plotScalingData$Consumers), 
#                                 max(plotScalingData$Consumers),
#                                 by = plotSamplingDataLM2Res) 
plotSamplingDataLM2Surf <- expand.grid(
  Basals = plotSamplingDataLM2AxisX,
  Consumers = plotSamplingDataLM2AxisY
) 
plotSamplingDataLM2Surf$CommunitySize <- exp(predict.lm(
  plotSamplingDataLM2, newdata = plotSamplingDataLM2Surf
))
plotSamplingDataLM2Surf <- reshape2::acast( # Cast to array/matrix
  plotSamplingDataLM2Surf, Basals ~ Consumers, value.var = "CommunitySize"
)

plotScaling %>% plotly::add_trace(z = plotSamplingDataLM2Surf,
                                  x = plotSamplingDataLM2AxisX,
                                  y = plotSamplingDataLM2AxisY,
                                  type = "surface")

minimal value for n is 3, returning requested palette with 3 different levels
minimal value for n is 3, returning requested palette with 3 different levels
minimal value for n is 3, returning requested palette with 3 different levels
minimal value for n is 3, returning requested palette with 3 different levels

Not particularly convincing, but it does agree with general ideas (consumers less important than basals).

plotSamplingDataLM3 <- lm(
  log(CommunitySize) ~ log(Basals) + log(Consumers) - 1, 
  data = plotScalingData
)
summary(plotSamplingDataLM3)

Call:
lm(formula = log(CommunitySize) ~ log(Basals) + log(Consumers) - 
    1, data = plotScalingData)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.80814 -0.13633  0.05056  0.40151  1.03117 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
log(Basals)     0.33969    0.02041  16.642  < 2e-16 ***
log(Consumers)  0.14852    0.01614   9.202 4.89e-14 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.4136 on 77 degrees of freedom
Multiple R-squared:  0.9598,    Adjusted R-squared:  0.9587 
F-statistic: 918.9 on 2 and 77 DF,  p-value: < 2.2e-16

# E.g. https://stackoverflow.com/a/38533046
plotSamplingDataLM3Res <- 3
plotSamplingDataLM3AxisX <- sort(unique(plotScalingData$Basals))
  # seq(min(plotScalingData$Basals), 
  #                               max(plotScalingData$Basals),
  #                               by = plotSamplingDataLM2Res) 
plotSamplingDataLM3AxisY <- sort(unique(plotScalingData$Consumers))
# seq(min(plotScalingData$Consumers), 
#                                 max(plotScalingData$Consumers),
#                                 by = plotSamplingDataLM2Res) 
plotSamplingDataLM3Surf <- expand.grid(
  Basals = plotSamplingDataLM3AxisX,
  Consumers = plotSamplingDataLM3AxisY
) 
plotSamplingDataLM3Surf$CommunitySize <- exp(predict.lm(
  plotSamplingDataLM3, newdata = plotSamplingDataLM3Surf
))
plotSamplingDataLM3Surf <- reshape2::acast( # Cast to array/matrix
  plotSamplingDataLM3Surf, Basals ~ Consumers, value.var = "CommunitySize"
)

plotScaling %>% plotly::add_trace(z = plotSamplingDataLM3Surf,
                                  x = plotSamplingDataLM3AxisX,
                                  y = plotSamplingDataLM3AxisY,
                                  type = "surface")

minimal value for n is 3, returning requested palette with 3 different levels
minimal value for n is 3, returning requested palette with 3 different levels
minimal value for n is 3, returning requested palette with 3 different levels
minimal value for n is 3, returning requested palette with 3 different levels

plotSamplingDataLM4 <- lm(
  CommunitySize ~ log(Basals) + log(Consumers), 
  data = plotScalingData
)
summary(plotSamplingDataLM4)

Call:
lm(formula = CommunitySize ~ log(Basals) + log(Consumers), data = plotScalingData)

Residuals:
   Min     1Q Median     3Q    Max 
-4.867 -1.628 -0.500  1.427  9.556 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)     0.09911    0.98519   0.101   0.9201    
log(Basals)     1.93666    0.16273  11.901   <2e-16 ***
log(Consumers)  0.26912    0.15390   1.749   0.0844 .  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.569 on 76 degrees of freedom
Multiple R-squared:  0.6525,    Adjusted R-squared:  0.6433 
F-statistic: 71.34 on 2 and 76 DF,  p-value: < 2.2e-16

# E.g. https://stackoverflow.com/a/38533046
plotSamplingDataLM4Res <- 3
plotSamplingDataLM4AxisX <- sort(unique(plotScalingData$Basals))
  # seq(min(plotScalingData$Basals), 
  #                               max(plotScalingData$Basals),
  #                               by = plotSamplingDataLM2Res) 
plotSamplingDataLM4AxisY <- sort(unique(plotScalingData$Consumers))
# seq(min(plotScalingData$Consumers), 
#                                 max(plotScalingData$Consumers),
#                                 by = plotSamplingDataLM2Res) 
plotSamplingDataLM4Surf <- expand.grid(
  Basals = plotSamplingDataLM3AxisX,
  Consumers = plotSamplingDataLM3AxisY
) 
plotSamplingDataLM4Surf$CommunitySize <- exp(predict.lm(
  plotSamplingDataLM4, newdata = plotSamplingDataLM4Surf
))
plotSamplingDataLM4Surf <- reshape2::acast( # Cast to array/matrix
  plotSamplingDataLM4Surf, Basals ~ Consumers, value.var = "CommunitySize"
)

plotScaling %>% plotly::add_trace(z = plotSamplingDataLM4Surf,
                                  x = plotSamplingDataLM4AxisX,
                                  y = plotSamplingDataLM4AxisY,
                                  type = "surface")

minimal value for n is 3, returning requested palette with 3 different levels
minimal value for n is 3, returning requested palette with 3 different levels
minimal value for n is 3, returning requested palette with 3 different levels
minimal value for n is 3, returning requested palette with 3 different levels

How do they interact with each other (on islands)?

# > runif(1) * 1E8
# [1] 82598679
set.seed(82598679)

mats <- list()
poolsall <- list() # name pools used in save data; be careful!

for (i in 1:length(dirViking)) {
  temp <- load(file.path(
    dirViking[i], 
    paste0("LawMorton1996-NumericalPoolCommunityScaling-PoolMats", 
           if (i > 1) i else "", 
           ".RDS")
  ))
  mats[[i]] <- eval(parse(text = temp[1]))
  poolsall[[i]] <- eval(parse(text = temp[2]))
}
pools <- poolsall

oldCandidateData <- load(file.path(getwd(), "candidateDataSoFar.Rdata"))
oldCandidateData <- eval(parse(text = oldCandidateData))

candidateData <- plotScalingData %>% dplyr::group_by(
  CombnNum, Dataset
) %>% dplyr::mutate(
  OtherSteadyStates = dplyr::n() - 1
) %>% dplyr::filter(
  OtherSteadyStates > 0
)
candidateData %>% dplyr::select(-CommunitySeq)

# First, check if it is in the paramFrame.
# Second, check if it is in the saved data from the previous.
# Otherwise, ignore it, we'll figure out what it is and why it is missing later.

candidateData$CommunityAbund <- ""

for (r in 1:nrow(candidateData)) {
  # ID 1:4 are used to identify paramFrame, 5 used to identify abundance
  ID <- candidateData[r, 1:6]
  paramFrameRow <- paramFrame %>% dplyr::filter(
    CombnNum == ID$CombnNum,
    Basals == ID$Basals,
    Consumers == ID$Consumers,
    Dataset == ID$Dataset
  )
  
  if (is.list(paramFrameRow$EndStateAbundance[[1]])) {
    entry <- which(ID$Communities == names(paramFrameRow$EndStateAbundance[[1]]))
    if (length(entry)) {
      candidateData$CommunityAbund[r] <- paramFrameRow$EndStateAbundance[[1]][[entry]]
      next()
    }
  }
  
  if (ID$Dataset == "2021-04") {
    
    oldCandDatRow <- oldCandidateData %>% dplyr::filter(
      CombnNum == ID$CombnNum,
      Basals == ID$Basals,
      Consumers == ID$Consumers,
      Communities == ID$Communities
    )
    
    if (nrow(oldCandDatRow) > 0) {
      if (oldCandDatRow$CommunityAbund != "") {
        candidateData$CommunityAbund[r] <- oldCandDatRow$CommunityAbund
      }
    }
  }
}

candidateData <- candidateData %>% dplyr::filter(CommunityAbund != "",
                                                 CommunityAbund != "Failure")

candidateData$CommunityProd <- NA
for (r in 1:nrow(candidateData)) {
  candidateData$CommunityProd[r] <- with(
    candidateData[r, ], 
    RMTRCode2::Productivity(
      Pool = pools[[DatasetID]][[CombnNum]], 
      InteractionMatrix = mats[[DatasetID]][[CombnNum]], 
      Community = Communities, 
      Populations = CommunityAbund
    )
  )
}

islandFUN <- function(i, dat, pool, mat, dmat) {
  temp <- dat[i, ]
  RMTRCode2::IslandDynamics(
    Pool = pool,
    InteractionMatrix = mat,
    Communities = c(
      list(temp$Communities[1]),
      rep("", nrow(dmat) - 2),
      temp$Communities[2]
    ),
    Populations = c(
      list(temp$CommunityAbund[1]),
      rep("", nrow(dmat) - 2),
      list(temp$CommunityAbund[2])
    ),
    DispersalPool = 0.0001,
    DispersalIsland = dmat,
  )
}

# For each group-dataset,
# For each pair,
# Run Island Dynamics,
# Save the result with its pairing
candidateData$TotalID <- paste(candidateData$CombnNum, candidateData$DatasetID)

islandInteractionsOneTwo <- list()

for (grp in unique(candidateData$TotalID)) {
  candidateDataSubset <- candidateData %>% dplyr::filter(TotalID == grp)
  
  if (nrow(candidateDataSubset) == 1) next()
  
  pairingResults <- combn(
    nrow(candidateDataSubset), 2, 
    islandFUN,
    dat = candidateDataSubset, 
    pool = pools[[
      candidateDataSubset$DatasetID[1]
      ]][[candidateDataSubset$CombnNum[1]]],
    mat = mats[[
      candidateDataSubset$DatasetID[1]
      ]][[candidateDataSubset$CombnNum[1]]],
    dmat = matrix(c(0, 1, 1, 0), nrow = 2, ncol = 2),
    simplify = FALSE
  )
  
  pairingResults <- lapply(
    pairingResults, function(mat, isles) {
      mat <- mat[nrow(mat), -1]
      retVal <- list()
      species <- length(mat) / isles
      for (i in 1:isles) {
        retVal[[i]] <- mat[((i - 1) * species + 1) : (i * species)]
      }
      retVal
    },
    isles = 2
  )
  
  islandInteractionsOneTwo[[grp]] <- pairingResults
}

islandInteractionsOneEmptyTwo <- list()

for (grp in unique(candidateData$TotalID)) {
  candidateDataSubset <- candidateData %>% dplyr::filter(TotalID == grp)
  
  if (nrow(candidateDataSubset) == 1) next()
  
  pairingResults <- combn(
    nrow(candidateDataSubset), 2, 
    islandFUN,
    dat = candidateDataSubset, 
    pool = pools[[
      candidateDataSubset$DatasetID[1]
      ]][[candidateDataSubset$CombnNum[1]]],
    mat = mats[[
      candidateDataSubset$DatasetID[1]
      ]][[candidateDataSubset$CombnNum[1]]],
    dmat = matrix(c(
      0, 1, 0, # Island 2 -> 1
      1, 0, 1, # Island 1 -> 2, Island 3 -> 2
      0, 1, 0  # Island 2 -> 3
    ), nrow = 3, ncol = 3, byrow = TRUE),
    simplify = FALSE
  )
  
  pairingResults <- lapply(
    pairingResults, function(mat, isles) {
      mat <- mat[nrow(mat), -1]
      retVal <- list()
      species <- length(mat) / isles
      for (i in 1:isles) {
        retVal[[i]] <- mat[((i - 1) * species + 1) : (i * species)]
      }
      retVal
    },
    isles = 3
  )
  
  islandInteractionsOneEmptyTwo[[grp]] <- pairingResults
}

# Format of table should be:
# ID, Community 1, Community 2, Outcomes 1-2, Outcomes 1-0-2
# For outcomes, species presence will be used.

communities <- NULL
totalCommunities <- NULL
for (grp in unique(candidateData$TotalID)) {
  candidateDataSubset <- candidateData %>% dplyr::filter(TotalID == grp)
  
  if (nrow(candidateDataSubset) > 1) {
    newCommunities <- combn(
      candidateDataSubset$Communities, 2, 
    )
    communities <- c(communities, newCommunities)
    totalCommunities <- c(
      totalCommunities,
      toString(sort(unique(unlist(lapply(newCommunities, 
                                         RMTRCode2::CsvRowSplit)))))
    )
  }
}

islandInteractionsOneTwoWhich <- unlist(lapply(
  seq_along(islandInteractionsOneTwo), function(i, x, tC) {
    lapply(x[[i]], function(y, tC) {
      lapply(y, function(z, tC) {
        toString(RMTRCode2::CsvRowSplit(tC)[which(z > 1E-6)])
      }, tC = tC)
      },
      tC = tC[i])
  },
  x = islandInteractionsOneTwo,
  tC = totalCommunities))

islandInteractionsOneEmptyTwoWhich <- unlist(lapply(
  seq_along(islandInteractionsOneEmptyTwo), function(i, x, tC) {
    lapply(x[[i]], function(y, tC) {
      lapply(y, function(z, tC) {
        toString(RMTRCode2::CsvRowSplit(tC)[which(z > 1E-6)])
      }, tC = tC)
      },
      tC = tC[i])
  },
  x = islandInteractionsOneEmptyTwo,
  tC = totalCommunities))


islandInteractionResults <- data.frame(
  DatasetID = rep(names(islandInteractionsOneTwo), 
                  unlist(lapply(islandInteractionsOneTwo, length))),
  Community1 = communities[seq(from = 1, to = length(communities), by = 2)],
  Community2 = communities[seq(from = 2, to = length(communities), by = 2)],
  OutcomeWOEmpty_Island1 = islandInteractionsOneTwoWhich[
    seq(from = 1, to = length(islandInteractionsOneTwoWhich), by = 2)],
  OutcomeWOEmpty_Island2 = islandInteractionsOneTwoWhich[
    seq(from = 1, to = length(islandInteractionsOneTwoWhich), by = 2)],
  OutcomeWEmpty_Island1 = islandInteractionsOneEmptyTwoWhich[
    seq(from = 1, to = length(islandInteractionsOneEmptyTwoWhich), by = 3)],
  OutcomeWEmpty_Island2 = islandInteractionsOneEmptyTwoWhich[
    seq(from = 1, to = length(islandInteractionsOneEmptyTwoWhich), by = 3)],
  OutcomeWEmpty_Island3 = islandInteractionsOneEmptyTwoWhich[
    seq(from = 1, to = length(islandInteractionsOneEmptyTwoWhich), by = 3)]
)

islandInteractionResults

islandInteractionResults %>% dplyr::mutate(
  C1WOInvaded = Community1 != OutcomeWOEmpty_Island1,
  C2WOInvaded = Community2 != OutcomeWOEmpty_Island2,
  C1WInvaded = Community1 != OutcomeWEmpty_Island1,
  C2WInvaded = Community2 != OutcomeWEmpty_Island3,
  StalemateWO = !C1WOInvaded & !C2WOInvaded,
  StalemateW = !C1WInvaded & !C2WInvaded,
  HybridWO = C1WOInvaded & C2WOInvaded,
  HybridW = C1WInvaded & C2WInvaded,
) %>% dplyr::select(-dplyr::starts_with("Outcome"))